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  1. Schedule… Discussion #6 – Things Practical

  2. Spiritual – Temporal 1 Nephi 15:32 32 And it came to pass that I said unto them that it was a representation of things both temporal and spiritual; for the day should come that they must be judged of their works, yea, even the works which were done by the temporal body in their days of probation. Mosiah 2:41 41 And moreover, I would desire that ye should consider on the blessed and happy state of those that keep the commandments of God. For behold, they are blessed in all things, both temporal and spiritual; and if they hold out faithful to the end they are received into heaven, that thereby they may dwell with God in a state of never-ending happiness. O remember, remember that these things are true; for the Lord God hath spoken it. Discussion #6 – Things Practical

  3. Lecture 6 – The Wheatstone Bridge An Applications of Things Electrical Discussion #6 – Things Practical

  4. c R1 R3 va vb a b + _ vs + vs R2 Rx _ d Wheatstone Bridge A circuit used to find: • An unknown resistance Rx • The unknown voltage vab • Another unknown value (such as a force) c R1 R3 a vb b va Rx R2 d Discussion #6 – Things Practical

  5. c R1 R3 va vb a b + vs R2 Rx _ d Wheatstone Bridge • The circuit consists of the parallel combination of 3 subcircuits with the same voltage: • The voltage source • Series combination of R1and R2 • Series combination of R3 and Rx • Voltage divider between: • R1and R2 • v2 = vad • R3 and Rx • vx = vbd Discussion #6 – Things Practical

  6. c R1 R3 va vb a b + vs R2 Rx _ d Wheatstone Bridge • KVL around the bottom loop: Discussion #6 – Things Practical

  7. c R1 R3 va vb a b + vs R2 Rx _ d Wheatstone Bridge • Example1: when is vab = 0? Discussion #6 – Things Practical

  8. c R1 R3 va vb a b + vs R2 Rx _ d Wheatstone Bridge • Example1: when is vab = 0? Discussion #6 – Things Practical

  9. c R1 R3 va vb a b + vs R2 Rx _ d Wheatstone Bridge • Find Rx: Discussion #6 – Things Practical

  10. c R1 R3 va vb a b + vs R2 Rx _ d Wheatstone Bridge • Example2: find Rx • R1 = R2 = R3 = 1kΩ, vs = 12V, vab = 12mV Discussion #6 – Things Practical

  11. c R1 R3 va vb a b + vs R2 Rx _ d Wheatstone Bridge • Example2: find Rx • R1 = R2 = R3 = 1kΩ, vs = 12V, vab = 12mV Discussion #6 – Things Practical

  12. Compression lower resistance Stretch higher resistance Resistance Strain Gauges • Strain gauge: device bonded to the surface of an object and whose resistance varies as a function of surface strain • Used to perform measurements of: • Strain • Stress, • Force • Torque • Pressure • NB: cylindrical resistance: • Compression/elongation will change resistance L – length of cylindrical resistor σ – conductivity of the resistor A – resistor cross-sectional area Discussion #6 – Things Practical

  13. Resistance Strain Gauges • Gauge factor (GF): the relationship between change in resistance and change in length • value of about 2 is common R0– the zero strain resistance • Strain (ε): the fractional change in length of an object • Max strain that can be measured is about 0.4 – 0.5 percent • i.e. ε = 0.004 to 0.005 • For a 120Ω resistor: +/– 1.2 Ω Discussion #6 – Things Practical

  14. RG Resistance Strain Gauges • Change in resistance due to strain: Circuit symbol for a strain gauge Discussion #6 – Things Practical

  15. c F ia L ib R1 R3 + _ vs h R1 a vb b va R4 w R4 R2 R2 & R3 d Wheatstone Bridge • Wheatstone bridge commonly used to measure force using strain gauge resistors • Example: force applied to a cantilever beam • Two strain gauges (R1 and R4) on top • Two strain gauges (R2 and R3) on bottom • Under no strain: R1 = R2 = R3 = R4= R0 Discussion #6 – Things Practical

  16. c R0 - ∆R R0 + ∆R F va vb L a b ia ib h R1 R4 + vs _ R0 - ∆R w R0 + ∆R R2 & R3 d Wheatstone Bridge • Under the strain of force F we have: tension compression compression tension Discussion #6 – Things Practical

  17. c R0 - ∆R R0 + ∆R F va vb L a b ia ib h R1 R4 + vs _ R0 - ∆R w R0 + ∆R R2 & R3 d Wheatstone Bridge • From elementary statics it can be shown that: Y is the beam’s modulus of elasticity Discussion #6 – Things Practical

  18. c R0 - ∆R R0 + ∆R c va vb ia ib a b R1 R3 + _ vs ia ib a vb b va + vs _ R0 - ∆R R4 R2 R0 + ∆R d d Wheatstone Bridge • Using Ohm’s Law: Discussion #6 – Things Practical

  19. c R0 - ∆R R0 + ∆R va vb a b ia ib + vs _ R0 - ∆R R0 + ∆R d Wheatstone Bridge • Using Ohm’s Law: Discussion #6 – Things Practical

  20. c R0 - ∆R R0 + ∆R va vb a b ia ib + vs _ R0 - ∆R R0 + ∆R d Wheatstone Bridge • Find vo in terms of force F: k is a calibration constant Discussion #6 – Things Practical

  21. F L h R1 R4 w R2 & R3 Wheatstone Bridge • Example3: using the Wheatstone bridge as a strain measurement tool find the maximum vo • the bridge measures forces ranging from 0 to 500 N • L = 0.3m, w = 0.05m, h = 0.01m, GF = 2, Y = 69x109N/m2, vs = 12V Discussion #6 – Things Practical

  22. F L h R1 R4 w R2 & R3 Wheatstone Bridge • Example3: using the Wheatstone bridge as a strain measurement tool find the maximum vo • the bridge measures forces ranging from 0 to 500 N • L = 0.3m, w = 0.05m, h = 0.01m, GF = 2, Y = 69x109N/m2, vs = 12V Discussion #6 – Things Practical

  23. Practical Sources Discussion #6 – Things Practical

  24. Ideal Sources • Ideal current source • 3A source • Ideal voltage source • 6V source Provides a prescribed voltage across its terminals irrespective of the current flowing through it. Provides a prescribed current irrespective of the voltage across it. Discussion #6 – Things Practical

  25. Practical Sources • Actual voltage sources have limitations • There is a limit to the number of total electrons any battery can motivate through a circuit • How to measure limitations? • Total number of electrons? (huge number) • Use coulombs? (also too huge) • amp-hour – unit invented for this purpose • 1 amp-hour = 1 amp for 1 hour = 2 amps for ½ hour = 1/3 amp for 3 hours • Batteries have ratings indicating their current limitations • Car battery – 12V, 70 amp-hours (A-h) @ 3.5 A (for 20 hours) • D – cell (1.5V) carbon-zinc battery – 4.6 amp-hours @ 100mA (for 46 hours) • 9 – volt carbon-zinc battery – 400 mA-hours @ 8mA (for 50 hours) 1 amp = 1 coulombs/second 1 amp-hour = 3600 coulombs Discussion #6 – Things Practical

  26. As RL 0, vs has to provide an infinite amount of current! Practical Sources • Actual voltage sources have limitations • As the load resistance (RL) decreases, the voltage source (vs) is required to provide increasing amounts of current (i) in order to maintain vs i + + v vs Load (RL) _ _ Discussion #6 – Things Practical

  27. is rs + vL – + Load (RL) vs _ Practical voltage source Practical Sources • Actual voltage sources have limitations A series resistance rs poses a limit to the maximum current the voltage source can provide Discussion #6 – Things Practical

  28. is rs + vL – + Load (RL) vs _ NB: vs = vL Practical voltage source Practical Sources • Actual voltage sources have limitations A series resistance rs poses a limit to the maximum current the voltage source can provide Discussion #6 – Things Practical

  29. + vs _ Practical Sources • Actual voltage sources have limitations A series resistance rs poses a limit to the maximum current the voltage source can provide is rs + vL – Practical voltage source Discussion #6 – Things Practical

  30. + vs – is Load (RL) As RL∞, is has to provide an infinite amount of voltage! Practical Sources • Actual current sources have limitations • As the load resistance (RL) increases, the current source (is) is required to provide increasing amounts of current (v) in order to maintain is Discussion #6 – Things Practical

  31. + vs – rs is Load (RL) Practical current source Practical Sources • Actual current sources have limitations A series resistance rs poses a limit to the maximum voltage the current source can provide Discussion #6 – Things Practical

  32. Practical Sources • Actual current sources have limitations A series resistance rs poses a limit to the maximum voltage the current source can provide + vs – rs is Practical current source Discussion #6 – Things Practical

  33. Practical Sources • Actual current and voltage sources have limitations Ideal 3A current source Ideal 6V votage source Discussion #6 – Things Practical

  34. Practical Sources • Actual current and voltage sources have limitations Practical 3A current source Practical 6V votage source Discussion #6 – Things Practical

  35. Measuring Devices Discussion #6 – Things Practical

  36. R Ω Ω Ohmmeter • Ohmmeter: measures the resistance of a circuit element NB: the resistance of an element can only be measured when the element is disconnected from all other circuit elements Ohmmeter connection setup for circuit element resistance measurement Ohmmeter symbol Discussion #6 – Things Practical

  37. R1 R1 A A + R2 _ vs + vs _ i i R2 Ammeter • Ammeter: a device that can measure the current flowing though a circuit element when connected in series with that circuit element NB: 1. the ammeter must be connected in series with the circuit element 2. the ammeter should not restrict the flow of current (i.e. cause a voltage drop) – an ideal ammeter has zero resistance Ammeter symbol Discussion #6 – Things Practical

  38. R1 + R2 – + v2 – V V + R2 – + vs + _ _ vs i i Voltmeter • Voltmeter: a device that can measure the voltage across a circuit element when connected in parallel with that circuit element NB: 1. the voltmeter must be connected in parallel with the circuit element 2. the voltmeter should not draw any current away from the element – an ideal voltmeter has infinite resistance R1 Voltmeter symbol Discussion #6 – Things Practical

  39. R1 W W + R2 – + _ vs i Wattmeter • Wattmeter: a device that can measure the power dissipated by a circuit element NB: 1. the wattmeter must be connected in parallel with the circuit element, but also in series with the circuit. – a wattmeter is simply the combination of a voltmeter and an ammeter R1 + R2 – Wattmeter symbol + vs _ i Discussion #6 – Things Practical

  40. rm rm V V A A Practical Voltmeters and Ammeters • In reality, voltmeters and ammeters have internal resistances • Practical ammeters will always add some resistance • Practical voltmeters will always draw some current Ideal Voltmeter Practical Voltmeter Ideal Ammeter Practical Ammeter Discussion #6 – Things Practical